1.9.2 Four-stage Runge-Kutta Method
Measurable Outcome 1.16, Measurable Outcome 1.17, Measurable Outcome 1.19
The most popular form of a four-stage Runge-Kutta method is:
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\(\displaystyle a\)
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\(\displaystyle =\)
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\(\displaystyle {\Delta t}f(v^ n, t^ n)\)
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(1.145) |
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\(\displaystyle b\)
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\(\displaystyle =\)
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\(\displaystyle {\Delta t}f(v^ n+a/2, t^ n + {\Delta t}/2)\)
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(1.146) |
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\(\displaystyle c\)
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\(\displaystyle =\)
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\(\displaystyle {\Delta t}f(v^ n+b/2, t^ n + {\Delta t}/2)\)
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(1.147) |
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\(\displaystyle d\)
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\(\displaystyle =\)
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\(\displaystyle {\Delta t}f(v^ n+c, t^ n + {\Delta t})\)
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(1.148) |
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\(\displaystyle v^{n+1}\)
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\(\displaystyle =\)
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\(\displaystyle v^ n + \frac{1}{6}(a + 2b + 2c + d)\)
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(1.149) |
Note that this method requires four evaluations of \(f\) per iteration. This method is fourth-order accurate, \(p=4\).
